This week in math 10 I learned how to solve systems of equations. A system of equations is when two equations are considered at the same time, which are then used to find the solution.  

Example 1: 

In this example we start off with the two equations y=3x-7 and y=-x+9. First, we input both of these into a graphing calculator. The graphing calculator will then graph both lines for us and we can identify the point where they intersect, x=4 y=5 these points are the solution. To verify that this is correct we can input the values back into either of the original equations. 5=3(4)-7. Now we will multiply 3 by 4 and minus 7, this will leave us with 5=5, meaning that we have successfully identified the solution. 

Example 2: 

Now in this example we are dealing with fractions which are a bit more difficult. We will start the same way as the first example by putting both of our equations into our graphing calculator which will graph both lines for us. Next we identify the place where they intersect, x=3 y=-1. Now we will input the 3 and –1 into either of our equations to verify that our solution is correct. Our new equation should look -1 is equal to  multiplied by 3 –. Now we must multiply by 3, which is 2.25. Now we will also solve –2.6 divided by 0.8, which is 3.25. Our equation should currently look like –1=2.25-3.25. Now we must finish it by subtracting 3.25 from 2.25 which is –1. This leaves our equation looking like –1=-1, this verifies that our solution was correct.